On the Maximal Sectorial Operators

TL;DR

This paper studies maximal sectorial operators, analyzing their spectral properties and eigenvalue behavior, and provides specific results for first-order differential operators in finite interval Hilbert spaces.

Contribution

It introduces a detailed description of maximal sectorial linear relations and investigates spectral discreteness and eigenvalue asymptotics, including a new result for first-order differential operators.

Findings

Spectral discreteness of maximal sectorial operators established

Eigenvalue asymptotic behavior characterized in terms of real parts

New results for first-order differential operators in finite interval Hilbert spaces

Abstract

In this work, firstly the maximal sectorial linear relations are described. Later on, the discreteness of the spectrum of the linear maximal sectorial operators and asymptotical behaviour of the eigenvalues of such operators in terms of the eigenvalues of its real part are investigated. Finally, it is obtained one result for the differential operators for first order in the Hilbert space of vector functions in finite interval.